Parameterized quantum circuits as universal generative models for continuous multivariate distributions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917508519297024 |
|---|---|
| author | Barthe, Alice Grossi, Michele Vallecorsa, Sofia Tura, Jordi Dunjko, Vedran |
| author_facet | Barthe, Alice Grossi, Michele Vallecorsa, Sofia Tura, Jordi Dunjko, Vedran |
| contents | Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several universality properties have been proven. However, in the case of quantum generative modelling, much less is known, especially when the task is to model distributions over continuous variables. In this work, we elucidate expectation value sampling-based models. Such models output the expectation values of a set of fixed observables from a quantum circuit into which classical random data has been uploaded. We prove the universality of such variational quantum algorithms for the generation of multivariate distributions. We explore various architectures which allow universality and prove tight bounds connecting the minimal required qubit number, and the minimal required number of measurements needed. Our results may help guide the design of future quantum circuits in generative modelling tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parameterized quantum circuits as universal generative models for continuous multivariate distributions Barthe, Alice Grossi, Michele Vallecorsa, Sofia Tura, Jordi Dunjko, Vedran Quantum Physics Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several universality properties have been proven. However, in the case of quantum generative modelling, much less is known, especially when the task is to model distributions over continuous variables. In this work, we elucidate expectation value sampling-based models. Such models output the expectation values of a set of fixed observables from a quantum circuit into which classical random data has been uploaded. We prove the universality of such variational quantum algorithms for the generation of multivariate distributions. We explore various architectures which allow universality and prove tight bounds connecting the minimal required qubit number, and the minimal required number of measurements needed. Our results may help guide the design of future quantum circuits in generative modelling tasks. |
| title | Parameterized quantum circuits as universal generative models for continuous multivariate distributions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.09848 |